Document Type
Report
Source Publication Title
Technical Report 277
Abstract
In this paper we study the behavior of a class of iterative algorithms for solving feasibility problems, that is finite systems of inequalities [see pdf for notation], where each [see pdf for notation] is a locally Lipschitz functional on a Hilbert space X. We show that, under quite mild conditions, the algorithms studied in this note, if converge, then they approximate a solution of the feasibility given problem, provided that the feasibility problem is consistent. We prove several convergence criteria showing that, when the envelope of the functionals [see pdf for notation], is sufficiently "regular", then the algorithms converge. The class of algorithms studied in this note contains, as special cases, many of the subgradient and projection methods of solving convex feasibility problems discussed in the literature.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
12-1-1990
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Butnariu, Dan, "Generalized Gradient Methods for Solving Locally Lipschitz Feasibility Problems" (1990). Mathematics Technical Papers. 335.
https://mavmatrix.uta.edu/math_technicalpapers/335